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Multiscale Modeling for the Statics of Nanostructures

Hoang, Kim-Quang; Kadapa, Chennakesava


Kim-Quang Hoang


Snehashish Chakraverty


Characterization of mechanical properties of materials is essential toward understanding their deformation behavior when subjected to external forces. For a complete understanding of the behavior of materials from the interaction of atoms at the nanoscale to their response at the macroscale using the continuum description, theoretical and computational tools that span a range of length and time scales are vital. To investigate the mechanical properties of novel materials, the recently proposed method of multiscale virtual power (MMVP) is adapted to derive finite element formulations for the micro-discrete to macro-continuum transition based on a discrete representative volume element (RVE) at the nanoscale. The discrete RVE comprises a cloud of atoms interacting among themselves through prescribed linear and nonlinear interatomic potentials and van derWaals forces. In this computational framework, the interactions among the atoms are modeled using nonlinear structural finite elements. The finite element implementation is coupled with the arc-length method to study the effect of damage arising from defects in the interatomic bonds and dislocations in the nanostructure. Determination of the macroscopic properties of the materials such as elastic moduli and strength are carried out by analyzing the homogenized tangent operators and acoustic tensor. The potential of the proposed multiscale framework for the characterization of nanomaterials is demonstrated using numerical examples that are applied to single-layer graphene, without and with defects. The results obtained using the proposed framework are in good agreement with those reported in the literature. With the ability to predict the continuum mechanical properties using micro-discrete to macro-continuum transition models, the proposed methodology proves to be a robust framework for the material characterization of novel nanomaterials.

Publication Date 2021-12
Deposit Date Aug 29, 2022
Publisher AIP Publishing
Pages 1-38
Book Title Nano Scaled Structural Problems: Static and Dynamic Behaviors
Chapter Number 2
ISBN 978-0-7354-2283-4
Public URL